Simplify the following expression: $ r = \dfrac{7}{10} + \dfrac{p + 1}{p - 6} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{p - 6}{p - 6}$ $ \dfrac{7}{10} \times \dfrac{p - 6}{p - 6} = \dfrac{7p - 42}{10p - 60} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{p + 1}{p - 6} \times \dfrac{10}{10} = \dfrac{10p + 10}{10p - 60} $ Therefore $ r = \dfrac{7p - 42}{10p - 60} + \dfrac{10p + 10}{10p - 60} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{7p - 42 + 10p + 10}{10p - 60} $ $r = \dfrac{17p - 32}{10p - 60}$